What are the solutions to the equation (x^2)/2+10/3 x=-2 ?

The solutions to the equation (x^2)/2+10/3 x=-2 are x=-2/3 ,x=-6

Find the zeros of (x^2)/2+10/3 x=-2

The zeros of (x^2)/2+10/3 x=-2 are x=-2/3 ,x=-6

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\frac{x ^{2}}{2} + \frac{10}{3} x = - 2

x = - \frac{2}{3}, x = - 6

Decimal Notation

x = - 0.66666 \dots, x = - 6

Solution steps

\frac{x ^{2}}{2} + \frac{10}{3} x = - 2

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

\frac{x ^{2}}{2} \cdot 6 + \frac{10}{3} x \cdot 6 = - 2 \cdot 6

Simplify

3 x^{2} + 20 x = - 12

Move

12

to the left side

3 x^{2} + 20 x + 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 20 \pm 2 0 ^{2} - 4 \cdot 3 \cdot 12}{2 \cdot 3}

2 0^{2} - 4 \cdot 3 \cdot 12 = 16

x_{1, 2} = \frac{- 20 \pm 16}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 20 + 16}{2 \cdot 3}, x_{2} = \frac{- 20 - 16}{2 \cdot 3}

x = \frac{- 20 + 16}{2 \cdot 3} : - \frac{2}{3}

x = \frac{- 20 - 16}{2 \cdot 3} : - 6

The solutions to the quadratic equation are:

x = - \frac{2}{3}, x = - 6

3 x^{2} - 24 x - 27 = 0

4 x^{2} - 24 x + 40 = 0

x^{2} - 17 x + 70 = 0

x^{2} - 5 x

x^{2} + 5 x + 6 = 0

What are the solutions to the equation (x^2)/2+10/3 x=-2 ?
The solutions to the equation (x^2)/2+10/3 x=-2 are x=-2/3 ,x=-6
Find the zeros of (x^2)/2+10/3 x=-2
The zeros of (x^2)/2+10/3 x=-2 are x=-2/3 ,x=-6